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Maximum weight induced matching in some subclasses of bipartite graphs

Author

Listed:
  • B. S. Panda

    (Indian Institute of Technology Delhi)

  • Arti Pandey

    (Indian Institute of Technology Ropar)

  • Juhi Chaudhary

    (Indian Institute of Technology Delhi)

  • Piyush Dane

    (Indian Institute of Technology Delhi)

  • Manav Kashyap

    (Indian Institute of Technology Delhi)

Abstract

A subset $$M\subseteq E$$ M ⊆ E of edges of a graph $$G=(V,E)$$ G = ( V , E ) is called a matching in G if no two edges in M share a common vertex. A matching M in G is called an induced matching if G[M], the subgraph of G induced by M, is the same as G[S], the subgraph of G induced by $$S=\{v \in V |$$ S = { v ∈ V | v is incident on an edge of $$M\}$$ M } . The Maximum Induced Matching problem is to find an induced matching of maximum cardinality. Given a graph G and a positive integer k, the Induced Matching Decision problem is to decide whether G has an induced matching of cardinality at least k. The Maximum Weight Induced Matching problem in a weighted graph $$G=(V,E)$$ G = ( V , E ) in which the weight of each edge is a positive real number, is to find an induced matching such that the sum of the weights of its edges is maximum. It is known that the Induced Matching Decision problem and hence the Maximum Weight Induced Matching problem is known to be NP-complete for general graphs and bipartite graphs. In this paper, we strengthened this result by showing that the Induced Matching Decision problem is NP-complete for star-convex bipartite graphs, comb-convex bipartite graphs, and perfect elimination bipartite graphs, the subclasses of the class of bipartite graphs. On the positive side, we propose polynomial time algorithms for the Maximum Weight Induced Matching problem for circular-convex bipartite graphs and triad-convex bipartite graphs by making polynomial time reductions from the Maximum Weight Induced Matching problem in these graph classes to the Maximum Weight Induced Matching problem in convex bipartite graphs.

Suggested Citation

  • B. S. Panda & Arti Pandey & Juhi Chaudhary & Piyush Dane & Manav Kashyap, 2020. "Maximum weight induced matching in some subclasses of bipartite graphs," Journal of Combinatorial Optimization, Springer, vol. 40(3), pages 713-732, October.
    • Handle: RePEc:spr:jcomop:v:40:y:2020:i:3:d:10.1007_s10878-020-00611-2
    DOI: 10.1007/s10878-020-00611-2
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    References listed on IDEAS

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    1. B. S. Panda & Arti Pandey & Juhi Chaudhary & Piyush Dane & Manav Kashyap, 0. "Maximum weight induced matching in some subclasses of bipartite graphs," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-20.
    2. Hao Chen & Zihan Lei & Tian Liu & Ziyang Tang & Chaoyi Wang & Ke Xu, 2016. "Complexity of domination, hamiltonicity and treewidth for tree convex bipartite graphs," Journal of Combinatorial Optimization, Springer, vol. 32(1), pages 95-110, July.
    3. Tian Liu & Zhao Lu & Ke Xu, 2015. "Tractable connected domination for restricted bipartite graphs," Journal of Combinatorial Optimization, Springer, vol. 29(1), pages 247-256, January.
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